Block-transitive Steiner 4-design with an almost simple automorphism group(具有几乎单型自同构群的区传递Steiner 4-设计)

Abstract

The classification of block-transitive t-design is a very interesting and important problem in the field of finite group and block design. The classification of block-transitive 2-design has been fully studied. But when t is greater than 3, the classification of block-transitive t-designs is still an open problem. In this paper, the classification problem of block transitive 4-designs is studied using the results of the classification of 2-homogeneous permutation groups. It is shown that if a Steiner 4-design admits an almost simple block-transitive automorphism group G, then G is either a typical simple group or G=M11 and D is a 4-(11,5,1) design or G=M23 and D is a 4-(23,7,1) design.区传递t-设计的分类是有限群与区组设计研究领域非常有趣且重要的问题。对区传递2-设计的分类已有比较充分的研究，但对t≥3的区传递t-设计的分类研究较少。利用2-齐次置换群的分类结论，研究了区传递4-设计的分类问题，证明了如果Steiner 4-设计D具有几乎单型区传递自同构群G，则要么G是典型单群，要么G=M11且D是4-(11,5,1)设计，或者G=M23且D是4-(23,7,1)设计。